SOLUTION: The total cost,C,(in thousands of dollars) to make reading glasses is
a function of the number of pairs of glasses made U(in thousands) and is given by C(u)= -0.02u^2 + 2.33u + 11
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-> SOLUTION: The total cost,C,(in thousands of dollars) to make reading glasses is
a function of the number of pairs of glasses made U(in thousands) and is given by C(u)= -0.02u^2 + 2.33u + 11
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Question 1200730: The total cost,C,(in thousands of dollars) to make reading glasses is
a function of the number of pairs of glasses made U(in thousands) and is given by C(u)= -0.02u^2 + 2.33u + 11.61
a)Find the marginal cost at the production level of 21 thousand and choose the correct units
b)What is the average cost at the same production level?
You can put this solution on YOUR website! **a) Find the Marginal Cost**
1. **Find the derivative of the cost function:**
* C'(u) = d/du (-0.02u² + 2.33u + 11.61)
* C'(u) = -0.04u + 2.33
2. **Evaluate the derivative at u = 21 (production level of 21 thousand pairs):**
* C'(21) = -0.04 * 21 + 2.33
* C'(21) = 1.49
**Therefore, the marginal cost at a production level of 21 thousand pairs of glasses is $1.49 thousand per thousand pairs (or $1490 per thousand pairs).**
**b) Find the Average Cost**
1. **Calculate the total cost at u = 21:**
* C(21) = -0.02 * (21)² + 2.33 * 21 + 11.61
* C(21) = -8.82 + 48.93 + 11.61
* C(21) = 51.72 thousand dollars
2. **Calculate the average cost:**
* Average Cost = Total Cost / Number of Units
* Average Cost = 51.72 thousand dollars / 21 thousand pairs
* Average Cost = 2.46 dollars per pair
**Therefore, the average cost at a production level of 21 thousand pairs of glasses is $2.46 per pair.**
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